$f(x) = 6x^{3}-4x^{2}+5x-3$ $g(n) = -4n+2(f(n))$ $ g(f(0)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(0)$ . Then we'll know what to plug into the outer function. $f(0) = 6(0^{3})-4(0^{2})+(5)(0)-3$ $f(0) = -3$ Now we know that $f(0) = -3$ . Let's solve for $g(f(0))$ , which is $g(-3)$ $g(-3) = (-4)(-3)+2(f(-3))$ To solve for the value of $g$ , we need to solve for the value of $f(-3)$ $f(-3) = 6(-3)^{3}-4(-3)^{2}+(5)(-3)-3$ $f(-3) = -216$ That means $g(-3) = (-4)(-3)+(2)(-216)$ $g(-3) = -420$